Maximum gap in (inverse) cyclotomic polynomial
- 주제(키워드) Cyclotomic polynomial , Inverse cyclotomic polynomial , Pairing-based cryptosystem
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press
- 발행년도 2012
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000093928
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jnt.2012.04.008
초록/요약
Let g(f) denote the maximum of the differences (gaps) between two consecutive exponents occurring in a polynomial f. Let Φ n denote the n-th cyclotomic polynomial and let Ψ n denote the n-th inverse cyclotomic polynomial. In this note, we study g(Φ n) and g(Ψ n) where n is a product of odd primes, say p 1<p 2<p 3, etc. It is trivial to determine g(Φp1), g(Ψp1) and g(Ψp1p2). Hence the simplest non-trivial cases are g(Φ p1p2) and g(Ψ p1p2p3). We provide an exact expression for g(Φ p1p2). We also provide an exact expression for g(Ψ p1p2p3) under a mild condition. The condition is almost always satisfied (only finite exceptions for each p 1). We also provide a lower bound and an upper bound for g(Ψ p1p2p3). © 2012 Elsevier Inc.
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